Question

If the product of two numbers is 20 and sum of their squares is 41, then find the ratio of the sum and the difference of the two numbers?
1. 9 ∶ 1
2. 1 ∶ 9
3. 9 ∶ 5
4. 4 ∶ 5

Answer 1

Correct Answer - Option 1 : 9 ∶ 1

Given:

Let the numbers be ‘x’ and ‘y’

∴ x × y = 20

x² + y² = 41

Formula used:

(x – y)² = x² + y² – 2xy

(x + y)² = x² + y² + 2xy

Calculation:

∵ (x – y)² = x² + y² – 2xy

⇒ (x – y)² = 41 – (2 × 20)

⇒ (x – y)² = 41 – 40

⇒ (x – y)² = 1

⇒ x – y = 1      ----(1)

∵ (x + y)² = x² + y² + 2xy

⇒ (x + y)² = 41 + (2 × 20)

⇒ (x + y)² = 41 + 40

⇒ (x + y)² = 81

⇒ x + y = √81 = 9      ----(2)

∴ (x + y) ∶ (x – y) = 9 ∶ 1